In a The 1985 articleComputer scientist Andrew YaoThe person will continue to win the AM Turing Award, confirming that among the hash tables there is a set of specific attributes, the best way to find an individual element or an empty point is to only go through potential points randomly, an approach called uniform exploration. He also stated that, in the worst case, where you are looking for the remaining last opening point, you can never do better x. Over 40 years, most computer scientists think that Yao's conjecture is right.
Krapivin was not retained by the usual wisdom for the simple reason that he did not know about it. I did this without knowing Yao's conjecture, he said. His discoveries with small suggestions have led to a new type of hash table, a person who does not rely on uniform exploration. And for this new hash table, the time needed for the query in the worst case and the inserted parts are proportional to (diary x)2—Far faster x. This result is directly contradictory with Yao's conjecture. Farach-Colton and Kuszmaul helped Krapivin to show that (login x)2 is the optimal limit, cannot be defeated for the popular chopping board that Yao wrote.
This result is very beautiful in that it solves and solves such a classic problem Guy Blelloch of Carnegie Mellon.
Not only they refused (Yao's conjecture), they also found the best answer possible for his question, he said Sepehr Assad of the University of Waterloo. We may have gone for 40 years before we know the correct answer.
In addition to rejecting Yao's conjecture, the new article also contains what many people consider to be a more incredible result. It involves a related situation, although a bit different: In 1985, Yao is not only at the worst time for the queries, but also at the average time done on all possible queries. He has proven that the hash table with certain attributes, including those who are labeled x.
Farach-Colton, Krapivin and Kuszmaul want to see whether the same limit is applied to green boards. They have shown that it is not by providing an example, a green hash x. In fact, it does not depend on x At all. You can get a actual figure that you can achieve continuous average query time, regardless of the entire hash table, completely surprised even for the authors.
The results of the group may not lead to any application immediately, but it is not all important, Conway said. It is important to understand these types of data structures better. You do not know when a result like this will unlock something that allows you to do better in reality.
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